The effect of hydrophilicity or hydrophobicity of polyelectrolyte on the interaction between polyelectrolyte and oppositely charged surfactants was investigated by using coarse-grained molecular dynamics simulations. The aggregation of surfactants on the hydrophilic polyelectrolyte is significantly different from that on the hydrophobic polyelectrolyte. The complexes evolve from the "bottle brush", through the "necklace", then to the micelle. However, the rod-like micelle, in which polyelectrolyte wraps around the micelle surface, only appears in the hydrophilic polyelectrolyte system. For the hydrophobic polyelectrolyte system, the spherical micelle is formed, and the polyelectrolyte penetrates into the hydrophobic core of complexes. The hydrophobic nature of the surfactant tails induces the surfactant's tendency to depart from the hydrophilic polyelectrolyte and point toward the bulk phase, but it is apt to combine with the hydrophobic polyelectrolyte, leading to a parallel configuration between the surfactants and the polyelectrolyte. When the charge ratio (Z) of surfactant to polylelectrolyte is lower, the polyelectrolyte shows extended structure, and with the increase of Z, the polyelectrolyte collapse undergoes either a continuous or an abrupt change depending on if it is a hydrophobic or hydrophilic polyelectrolyte. At higher charge density of the hydrophilic there is a synergistic effect of the electrostatic interaction between surfactant and polyelectrolyte, with the hydrophobic interaction among the adsorbed surfactants. For the hydrophobic polyelectrolyte system, no synergistic effect is observed.